Free-Space Path Loss Calculator
Calculate ideal free-space path loss from RF frequency and distance, solve the reverse distance or frequency, and compare two line-of-sight RF links under the same isotropic reference model.
This calculator only covers the propagation path-loss term. It does not include transmit power, antenna gain, cable loss, receiver sensitivity, link margin, terrain, penetration loss, rain fade, multipath or Fresnel-zone clearance.
Engineering tool
Free-Space Path Loss Calculator
Calculate ideal free-space path loss from frequency and distance, solve maximum distance or frequency, and compare two ideal RF links.
Result console
- Free-Space Path Loss
- 80.052008 dB
- Wavelength
- 12.491352 cm
- Frequency Used
- 2.4 GHz
- Distance Used
- 100 m
- Linear Path-Loss Ratio
- 1.012047e+8Pt / Pr
- Ideal Power Transfer Ratio
- 9.880961e-9Pr / Pt
- Ideal Power Transfer
- 9.880961e-7%
- Formula Used
- FSPL = 20log10(4πdf / c)
Free-space path loss assumes ideal line-of-sight propagation and isotropic reference antennas. It does not include transmit power, antenna gain, cable loss, fading, terrain, buildings, rain or receiver sensitivity.
Formula reference
Free-Space Path Loss Formulas
Internal calculations use SI units: hertz, meters, meters per second, dimensionless ratios and dB.
λ = c / fFSPL = 20 × log10(4πd / λ)FSPL = 20 × log10(4πdf / c)FSPL(dB) ≈ 32.44 + 20log10(dkm) + 20log10(fMHz)FSPL(dB) ≈ 92.45 + 20log10(dkm) + 20log10(fGHz)d = c / (4πf) × 10^(FSPL / 20)f = c / (4πd) × 10^(FSPL / 20)Llinear = 10^(FSPL / 10)Pr / Pt = 10^(-FSPL / 10)Variable definitions
- FSPL
- ideal free-space path loss in dB
- d
- transmitter-to-receiver separation distance in meters
- f
- RF frequency in hertz
- λ
- wavelength in meters
- c
- speed of light, 299,792,458 m/s
- Llinear
- transmitted-to-received isotropic free-space power ratio
- Pt
- transmit power reference in the ideal Friis proportional term
- Pr
- receive power reference in the ideal Friis proportional term
- π
- mathematical constant pi
- This calculator does not add antenna gain or system loss terms.
Worked Examples
100 MHz over 1 km
FSPL = 32.4478 + 20log10(1 km) + 20log10(100 MHz) = 72.4478 dB. Wavelength is 2.9979 m.
433 MHz over 1 km
Using the SI formula, FSPL = 85.1775 dB. Wavelength is 0.692361 m.
915 MHz over 1 km
Using the SI formula, FSPL = 91.6762 dB. Wavelength is 0.327642 m.
2.4 GHz over 100 m
FSPL = 80.0520 dB. Wavelength is 0.124914 m and the ideal power transfer ratio is about 9.881e-9.
2.4 GHz over 1 km
FSPL = 100.0520 dB. Increasing distance from 100 m to 1 km adds exactly 20 dB in the ideal model.
5.8 GHz over 1 km
FSPL = 107.7163 dB. Wavelength is 0.051688 m.
Maximum distance
At 2.4 GHz with 100 dB allowed FSPL, d = c / (4πf) × 10^(100/20), or about 994.03 m.
Calculate frequency
At 1 km with 100 dB FSPL, f = c / (4πd) × 10^(100/20), or about 2.386 GHz.
Compare distance increase
At 2.4 GHz, 200 m has 6.0206 dB more FSPL than 100 m. The linear loss ratio difference is 4.
Compare frequency increase
At the same distance, 2 GHz has 6.0206 dB more FSPL than 1 GHz under isotropic assumptions.
Engineering Notes
- FSPL increases as distance increases. Doubling distance adds about 6.0206 dB, and increasing distance by 10 times adds 20 dB.
- At the same distance and isotropic reference, doubling frequency adds about 6.0206 dB, and increasing frequency by 10 times adds 20 dB.
- FSPL is not cable loss, antenna loss, mismatch loss, or air absorption. It describes geometric spreading of an electromagnetic wave.
- Real wireless propagation may include multipath, shadowing, diffraction, ground reflection, building penetration, foliage loss, rain attenuation, atmospheric absorption and polarization mismatch.
- Ideal free-space conditions usually do not fully represent indoor, urban, forest, low-altitude ground or non-line-of-sight links.
- The model is usually applied in far-field conditions. Very short distances or large antennas may require a different near-field treatment.
- Coverage range must be evaluated with transmit power, antenna gains, receiver sensitivity, fade margin, interference, regulations and antenna height.
- When physical antenna aperture or gain changes with frequency, system-level comparisons can differ from a simple equal-gain FSPL comparison.
Common Mistakes
- Putting meters into the MHz/km constant formula.
- Using GHz where the formula expects MHz.
- Confusing FSPL with coaxial cable attenuation.
- Assuming FSPL means energy is absorbed by air.
- Ignoring antenna gain and treating FSPL as a complete link budget.
- Assuming ideal maximum distance equals real coverage distance.
- Ignoring receiver sensitivity, fade margin, obstacles and multipath.
- Thinking frequency doubling doubles loss instead of adding about 6.0206 dB.
- Ignoring near-field limits at very short distances.
- Multiplying linear loss ratios and dB values as if they were the same kind of quantity.
FSPL, Friis and Link Budget Boundary
Friis transmission equation is Pr = Pt × Gt × Gr × (λ / 4πd)². When Gt = 1 and Gr = 1, the ideal power ratio becomes Pr / Pt = (λ / 4πd)². The inverse is the free-space path-loss linear ratio, LFS = (4πd / λ)², and FSPL = 20log10(4πd / λ).
RF-004 calculates FSPL and ideal proportional terms only. RF-005 is reserved for a general link budget with transmit power, antenna gains, cable losses, path loss, receiver sensitivity and link margin. RF-012 is reserved for ideal Friis received-power calculation with transmit power and antenna gains.
Support reference
FAQ
What is free-space path loss?
Free-space path loss is the ideal geometric spreading loss between two points in unobstructed free space. It describes how power density decreases with distance and frequency in the isotropic Friis reference model.
How do I calculate FSPL?
Use FSPL = 20log10(4πdf / c), where distance is in meters, frequency is in hertz, and c is the speed of light. The common MHz/km form is approximately 32.44 + 20log10(dkm) + 20log10(fMHz).
Why does path loss increase with distance?
In free space, electromagnetic energy spreads over a larger spherical area as distance increases. Doubling distance increases FSPL by about 6.0206 dB, and increasing distance by 10 times adds 20 dB.
Why does path loss increase with frequency?
For the same distance and isotropic antenna reference, higher frequency means shorter wavelength and a smaller Friis power-transfer term. Doubling frequency increases FSPL by about 6.0206 dB.
What is the difference between FSPL and link budget?
FSPL is only the ideal propagation path-loss term. A link budget also includes transmit power, antenna gains, cable losses, receiver sensitivity, implementation losses and fade margin.
Does FSPL include antenna gain?
No. FSPL is calculated before antenna gain is added. Antenna gains are handled in a full link budget or Friis received-power calculation.
Does FSPL include cable loss?
No. Cable loss is a separate attenuation term caused by transmission-line loss. It is not the same as free-space path loss.
Can FSPL predict real wireless range?
Not by itself. Real range depends on transmit power, antenna gains, receiver sensitivity, fade margin, terrain, obstacles, interference, polarization, regulations and installation details.
What is the difference between FSPL and the Friis transmission equation?
FSPL is the loss term from the Friis equation. Friis received power also includes transmit power and antenna gains. RF-004 calculates FSPL only; RF-012 is reserved for ideal Friis received power.
Does free-space path loss mean energy is absorbed by the air?
No. FSPL primarily describes geometric spreading in ideal free space. Atmospheric absorption, rain fade and building penetration are separate effects.
When does the free-space model become inaccurate?
The model becomes less representative in near-field conditions, indoor or urban environments, obstructed links, multipath, diffraction, ground reflection, foliage, rain, atmospheric absorption or non-line-of-sight paths.
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Future Engineering Guide Topics
Free-Space Path Loss Explained
In_DevelopmentFriis Transmission Equation Explained
In_DevelopmentHow Distance and Frequency Affect RF Path Loss
In_DevelopmentHow to Build an RF Link Budget
In_DevelopmentNear Field vs Far Field
In_DevelopmentUnderstanding Wireless Fade Margin
In_DevelopmentDisclaimer
This calculator provides ideal free-space propagation estimates only. It does not replace RF link-budget design, site survey, regulatory review, antenna measurement, receiver testing, safety analysis, or field validation.